I am glad that you are enthusiastic in your pursuit of the idea you have proposed concerning the nature of gravity. It is people like you that advance the fields of known science, and I would like to do as much as I can to help you further develop your hypothesis. For this post, I shall only discuss your use of the mass-energy equivalence theory of Einstein.

Matter interacts with other matter and the universe through energy. In fact, matter is made up of energy. We also know that matter, if it comes into contact with antimatter, blows up into energy instantly. That is where the problem of anti-energy and a proposal of something along the lines of anti-mass-anti-energy equivalence arises.

Gravity is an attractive force, both to matter and anti-matter. Both of these forms of particles have mass, and mass is what gravity acts upon. Also, since matter and anti-matter annihilate into energy, not energy and anti-energy, it goes to conclude that anti-matter is equivalent to energy, as well, and that gravity really is a form of energy, not anti-energy.

Based on the above conclusion, there is in fact no need to postulate anti-energy, at least not in order to explain how anti-matter can interact. I'm not proposing that anti-energy can't possibly exist, but based on E=mc2, it is unnecessary. Gravity attracts matter and anti-matter indiscriminately, and so does energy.